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Understanding 3D Sound and Spatial Audio: Intensity Panning with Loudspeakers

This document explores the principles of intensity panning in stereo sound systems, utilizing the Law of Sines to analyze how virtual images are created by adjusting the sound levels from left and right speakers. It delves into the mathematical relationships that describe amplitude and phase differences, the effects of crosstalk, and the impact of room acoustics on perceived sound. The study emphasizes the importance of interaural time differences (ITD) and interaural intensity differences (IID) in sound localization and compares various panning methodologies for different acoustic environments.

andrew-slater
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Understanding 3D Sound and Spatial Audio: Intensity Panning with Loudspeakers

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  1. 3-D Sound and Spatial Audio MUS_TECH 348

  2. Intensity Panning with Loudspeakers

  3. Stereo Law of Sines sin (ß) / sin (q) = (L - R ) / (L + R) Where ß is the angle of the virtual image and q is the angle of the loudspeaker from center “Phaser Analysis of Some Stereophonic Phenomena” Ben Bauer 1961

  4. By the way, just HOW does panning work? L R Panning with stereo loudspeakers includes crosstalk!

  5. a a t t a t Consider sine waves! a t L R Panning results in amplitude and phase difference!

  6. Consider sine waves! L sin (2p f t) R sin (2p f t) k (<1) and ø are constant for fixed loudspeaker & listener locations L sin (2p f t) + kR sin (2p f t + ø) L * R --- delayed (ø ) and reduced in gain (k) * + t t = t

  7. Consider sine waves! a t a t L R R sin (2p f t) + kL sin (2p f t + ø) L sin (2p f t) + kR sin (2p f t + ø) What about the resulting IID and ITD?

  8. a t Consider sine waves! a t L R ( L2 + k2R2 + 2 kLR cos (- ø) ) IID(in decibels) = 10 log (k2L2 + R2 + 2 kLR cos (- ø) ) L sin(2pft) + R sin(2pft+ ø) L cos(2pft) + R cos(2pft+ ø) Interaural phase = arctan R and L affect the IID and interaural phase!

  9. Panning Methods 0.5 amp Amplitude Panning L (C) R position 0.7 Intensity or Power Panning amp L (C) R position

  10. Panning Methods Near-field Monitoring: Greatest accuracy: Low Frequencies: amplitude panning High Frequencies: power panning Large-space Monitoring: power panning

  11. Panning Inaccuracy High Low L (C) R position

  12. How well does panning work in typical multichannel settings like 5.1? L C R S1 S2 S1 S2 S1 S2 S1 S2

  13. ITD / IID HRTF For side locations the only change is a cross fading of HRTFs! Cross fading does not produce proper HRTFs in the middle! HRTF only HRTF ITD / IID

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